The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with a mean of 1261 chips and a standard deviation of 118 chips.

​(a) Determine the 29th percentile for the number of chocolate chips in a bag.

​(b) Determine the number of chocolate chips in a bag that make up the middle 96​% of bags.

​(c) What is the interquartile range of the number of chocolate chips in a bag of chocolate chip​ cookies?

Win/Loss and With/Without Joe: Joe plays basketball for the Wildcats and missed some of the season due to an injury. The win/loss record with and without Joe is summarized in the contingency table below.

Observed Frequencies: O_i's

The Test: Test for a significant dependent relationship between wins/losses and whether or not Joe played. Conduct this test at the 0.01 significance level.

(a) What is the test statistic? Round your answer to 3 decimal places.

χ²

=

(b) What is the conclusion regarding the null hypothesis?

reject H₀ fail to reject H₀    

(c) Choose the appropriate concluding statement.

We have proven that Joe causes the team to do better. The evidence suggests that the outcome of the game is dependent upon whether or not Joe played.      There is not enough evidence to conclude that the outcome of the game is dependent upon whether or not Joe played. We have proven that the outcome of the game is independent of whether or not Joe played.

Changes in Education Attainment: According to the U.S. Census Bureau, the distribution of Highest Education Attainment in U.S. adults aged 25 - 34 in the year 2005 is given in the table below.

Census: Highest Education Attainment - 2005

In a survey of 4000 adults aged 25 - 34 in the year 2013, the counts for these levels of educational attainment are given in the table below.

Survey (n = 4000): Highest Education Attainment - 2013

The Test: Test whether or not the distribution of education attainment has changed from 2005 to 2013. Conduct this test at the 0.01 significance level.(a) What is the null hypothesis for this test?

H₀: p₁ = p₂ = p₃ = p₄ = p₅ = 1/5 H₀: The probabilities are not all equal to 1/5.     H₀: p₁ = 0.14, p₂ = 0.48, p₃ = 0.08, p₄ = 0.22, and p₅ = 0.08. H₀: The distribution in 2013 is different from that in 2005.

(b) The table below is used to calculate the test statistic. Complete the missing cells.
Round your answers to the same number of decimal places as other entries for that column.

(c) What is the value for the degrees of freedom? 7
(d) What is the critical value of

χ²

? Use the answer found in the

χ²

-table or round to 3 decimal places.
t_α = 8

(e) What is the conclusion regarding the null hypothesis?

reject H₀ fail to reject H₀    

(f) Choose the appropriate concluding statement.

We have proven that the distribution of 2013 education attainment levels is the same as the distribution in 2005. The data suggests that the distribution of 2013 education attainment levels is different from the distribution in 2005.      There is not enough data to suggest that the distribution of 2013 education attainment levels is different from the distribution in 2005.

1. Resveratrol, an ingredient in red wine and grapes, has been shown to promote weight loss in rodents. One study investigates whether the same phenomenon holds true in primates. The grey mouse lemur, a primate, demonstrates seasonal spontaneous obesity in preparation for winter, doubling its body mass. A sample of six lemurs had their resting metabolic rate, body mass gain, food intake, and locomotor activity measured for one week prior to resveratrol supplementation (to serve as a baseline) and then the four indicators were measured again after treatment with a resveratrol supplement for four weeks. Some p-values for tests comparing the mean differences in these variables are given below. In parts a-d, state the conclusion of the test using a 5% significance level, and interpret the conclusion in context. (HINT: For thinking of the null/alternative hypothesis, the null would be that there is no change and the alternative would be what they are trying to test as described in the wording in each part)

a. In a test to see if mean resting metabolic rate is higher after treatment, p=0.013

b. In a test to see if mean body mass gain is lower after treatment, p=0.007

c. In a test to see if mean food intake is affected by the treatment, p=0.035

d. In a test to see if locomotor activity is affected by the treatment, p=0.980

e. In which test is the strongest evidence for rejecting the null found? The weakest? f. How do your answers to parts a-d change if the researchers make their conclusions using a stricter 1% significance level?

Choosing Lottery Numbers: In the Super-Mega lottery there are 50 numbers (1 to 50), a player chooses ten different numbers and hopes that these get drawn. If the player's numbers get drawn, he/she wins an obscene amount of money. The table below displays the frequency with which classes of numbers are chosen (not drawn). These numbers came from a sample of 180 chosen numbers.

Chosen Numbers (n = 180)

The Test: Test the claim that all chosen numbers are not evenly distributed across the five classes. Test this claim at the 0.01 significance level.

(a) The table below is used to calculate the test statistic. Complete the missing cells.
Round your answers to the same number of decimal places as other entries for that column.

(b) What is the value for the degrees of freedom? 6
(c) What is the critical value of

χ²

? Use the answer found in the

χ²

-table or round to 3 decimal places.
t_α = 7

(d) What is the conclusion regarding the null hypothesis?

reject H₀ fail to reject H₀    

(e) Choose the appropriate concluding statement.

We have proven that all chosen numbers are evenly distributed across the five classes. The data supports the claim that all chosen numbers are not evenly distributed across the five classes.      There is not enough data to support the claim that all chosen numbers are not evenly distributed across the five classes.

Suppose that you want to estimate the mean time it takes drivers to react following the application of brakes by the driver in front of them. You take a sample of reaction time measurements and compute their mean to be 2.5 seconds and their standard deviation to be 0.4 seconds. For each of the following sampling scenarios, determine which test statistic is appropriate to use when making inference statements about the population mean.

Before calculating a correlation coefficient, explain why you would create and examine a scatterplot of the relationship. In your response, please discuss (a) linearity (b) homoscedasticity, (c) restriction of range, and (d) the presence of outliers.

Which of the following statements is true?

Migraine and Acupuncture: A migraine is a particularly painful type of headache, which patients sometimes wish to treat with acupuncture. To determine whether acupuncture relieves migraine pain, researchers conducted a randomized controlled study where 166 patients diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control. 67 patients in the treatment group received acupuncture that is specifically designed to treat migraines. 99 patients in the control group received placebo acupuncture (needle insertion at non-acupoint locations). 24 hours after patients received acupuncture, they were asked if they were pain free. Results are summarized in the contingency table below. Test to see if migraine pain relief is dependent on receiving acupuncture. Use αα = 0.05.

a) What is the correct null hypothesis?

• H0H0: p1≠p2≠p3≠p4p1≠p2≠p3≠p4
• H0H0: p1=p2=p3=p4p1=p2=p3=p4
• H0H0: Migraine pain relief is dependent on receiving acupuncture.
• H0H0: Migraine pain relief is independent on receiving acupuncture.

b) Fill in the expected values, round answers to at least 4 decimal places.

c) Find the test statistic, round answer to at least 4 decimal places.

d) What is the p-value?

e) What is the correct conclusion?

• There is no statistical evidence that migraine pain relief is dependent on receiving acupuncture.
• There is statistical evidence that migraine pain relief is dependent on receiving acupuncture.

2. A researcher is interested in testing the relationship between the amount of fat in one's diet and the development of cancer (of any type).

a. What is the research hypothesis? What is the null hypothesis?

b. How will the researcher determine whether or not there is a relationship between dietary fat and cancer? What steps will the researcher take?

c. Assume that the researcher made an error of the second type (i.e., a type II error). What did the researcher do to make this error?

the data set shown​ below, complete parts​ (a) through​ (d) below. x 3 4 5 7 8 y 5 7 6 12 13 ​(a)  Find the estimates of beta 0 and beta 1. beta 0almost equalsb 0equals nothing ​(Round to three decimal places as​ needed.) beta 1almost equalsb 1equals nothing ​(Round to three decimal places as​ needed.)(a)  Find the estimates of beta 0 and beta 1. beta 0almost equalsb 0equals ??​(Round to three decimal places as​ needed.) beta 1almost equalsb 1equals ?? ​(Round to three decimal places as​ needed.) ​(b)  Compute the standard​ error, the point estimate for sigma. s Subscript eequals ??? ​(Round to four decimal places as​ needed.) ​(c)  Assuming the residuals are normally​ distributed, determine s Subscript b 1 Baseline . s Subscript b 1equals ??? ​(Round to three decimal places as​ needed.) ​(d)  Assuming the residuals are normally​ distributed, test Upper H 0 : beta 1 equals 0 versus Upper H 1 : beta 1 not equals 0 at the alpha equals 0.05 level of significance. Use the​ P-value approach. The​ P-value for this test is ????​(Round to three decimal places as​ needed.) Make a statement regarding the null hypothesis and draw a conclusion for this test. Choose the correct answer below. A. Reject Upper H 0. There is sufficient evidence at the alpha equals 0.05 level of significance to conclude that a linear relation exists between x and y. Do not reject Upper H 0. There is sufficient evidence at the alpha equals 0.05 level of significance to conclude that a linear relation exists between x and y. C. Reject Upper H 0. There is not sufficient evidence at the alpha equals 0.05 level of significance to conclude that a linear relation exists between x and y. D. Do not reject Upper H 0. There is not sufficient evidence at the alpha equals 0.05 level of significance to conclude that a linear relation exists between x and y.

Lafayette Public School System has three high schools to serve a district divided into five areas. The capacity of each high school, the student population in each area, and the distance (in miles) between each school and the center of each area are listed in the table below:

(Part a - 8 points) Formulate and list the linear program for the above problem to minimize the total student-miles traveled per day. You do NOT need to solve your listed linear program.  

(Part b - 2 points) If Capedot High School will be closed to conserve the school system’s resources and its budget, how will you efficiently revise your linear program to cope with this school closing?

Please use Word or something to write your answer and show work. Thank you very much! :D

Identify two important operating standards that are routinely measured in your organization. These measures must meet the criteria for qualitative, nominal measures. Observations must be cross-classified into a contingency table. Obtain a sample that will produce at least five observations into each group of the cross-classification.

Purpose:  To demonstrate the application of non-parametric tests in your organization.

Example:  A standard measure that fits these requirements is the human resource department’s employee tracking system. The director of human resources of my company wants to do a study to determine if there is a relationship between the management status and gender of the employees. She creates a contingency table that has Male or Female categories for the rows, and Manager or non-manager categories for the columns. Then she counts the number of female managers, female non-managers, male managers, and male non-managers and enters the numbers in the table. This is the observed value table. Then she conducts the hypothesis test.

a)      Perform the cross-classification of the two nominal variables into a contingency table.

b)       Test the hypothesis that there is no relationship between the two variables.

c)       Discuss the result and interpretation of your hypothesis test

height and head circumference. The data are summarized below. Complete parts​ (a) through​ (f) below.

​(a) Treating height as the explanatory​ variable, x, use technology to determine the estimates of

beta 0β0

and

beta 1β1.

beta 0β0almost equals≈b 0b0equals=

nothing ​(Round to four decimal places as​ needed.)beta 1β1almost equals≈b 1b1equals=

nothing ​(Round to four decimal places as​ needed.)

B Use technology to compute the standard error of the​ estimate,

s Subscript ese.

s Subscript eseequals=

​(Round to four decimal places as​ needed.)

​(c) A normal probability plot suggests that the residuals are normally distributed. Use technology to determine

s Subscript b 1sb1.

s Subscript b 1sb1equals=  

​(Round to four decimal places as​ needed.)

​(d) A normal probability plot suggests that the residuals are normally distributed. Test whether a linear relation exists between height and head circumference at the

alphaαequals=0.010.01

level of significance. State the null and alternative hypotheses for this test.

Choose the correct answer below.

A.

Upper H 0H0​:

beta 1β1equals=0

Upper H 1H1​:

beta 1β1not equals≠0

Your answer is correct.

B.

Upper H 0H0​:

beta 1β1equals=0

Upper H 1H1​:

beta 1β1greater than>0

C.

Upper H 0H0​:

beta 0β0equals=0

Upper H 1H1​:

beta 0β0greater than>0

D.

Upper H 0H0​:

beta 0β0equals=0

Upper H 1H1​:

beta 0β0not equals≠0

Determine the​ P-value for this hypothesis test.

​P-valueequals=

​(Round to three decimal places as​ needed.)

What is the conclusion that can be​ drawn?

A.

RejectReject

Upper H 0H0

and conclude that a linear relation

existsexists

between a​ child's height and head circumference at the level of significance

alphaαequals=0.010.01.

Your answer is correct.

B.

Do not rejectDo not reject

Upper H 0H0

and conclude that a linear relation

does not existdoes not exist

between a​ child's height and head circumference at the level of significance

alphaαequals=0.010.01.

C.

RejectReject

Upper H 0H0

and conclude that a linear relation

does not existdoes not exist

between a​ child's height and head circumference at the level of significance

alphaαequals=0.010.01.

D.

Do not rejectDo not reject

Upper H 0H0

and conclude that a linear relation

existsexists

between a​ child's height and head circumference at the level of significance

alphaαequals=0.010.01.

​(e) Use technology to

construct

a​ 95% confidence interval about the slope of the true​ least-squares regression line.

Lower​ bound:

Upper​ bound: 0.351

​(Round to three places as​ needed.)

​(f) Suppose a child has a height of 26.5 inches. What would be a good guess for the​ child's head​ circumference?

A good stimate of the​ child's head circumference would be inches.

​(Round to two decimal places as​ needed.)

Please answer all parts of the problem, if possible.

Let X ~ Binomial (1, p)  0 <p<1 a. Show explicitly that this family is “very regular,” that is, that R0,R1,R2,R3,R4 hold.

R 0 - different parameter values have different functions.

R 1 - parameter space does not contain its own endpoints.

R 2. - the set of points x where f (x, p) is not zero and should not depend on p.

R 3. One derivative can be found with respect to p.

R 4. Two derivatives can be found with respect to p.

b. Find the maximum likelihood estimator of p, call it Yn for this problem.

c. Is Yn unbiased? Explain.

d. Show that Yn is consistent asymptotically normal and identify the asymptotic normal variance.

e. Variance-stabilize your result in (d) or show there is no need to do so.

f. Compute I (p) where I is Fisher’s Information. g. Compute the efficiency of Yn for p (or show that you should not!).